Neuromorphic computing takes inspiration from the brain to build highly parallel, energy- and area-efficient architectures. Recently, hardware realizations of neurons and synapses using memristive devices were proposed and applied for the task of correlation detection. However, for weakly correlated signals, this task becomes challenging because of the variability and the asymmetric conductance response of the memristive devices. In this paper, we propose a high-density memristive system realized using nanodevices based on phase-change technology. We present a noise-robust phase-change implementation of a neuron, and a synaptic learning rule that is capable of capturing patterns of weakly correlated inputs. We experimentally demonstrate operation with a correlation coefficient as low as 0.2 using a record number of 1M phase-change synapses.